#include <iostream>
#include <sstream>
#include <algorithm>
#include <cmath>
using namespace std;
typedef unsigned long LONG;
const LONG primes[] = { 
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,
149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,
293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,
461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,
641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821
,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,
1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,
1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,
1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,
1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,
1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,
1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,
2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,
2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,
2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,
2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,
2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,
3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,
3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,
3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,
3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,
3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,
3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,
4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,
4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,
4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,
4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,
5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,
5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,
5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,
5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,
5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,
5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,
6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,
6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,
6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,
6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,
7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,
7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,
7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,
7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,
7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,
8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,
8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,
8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,
8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,
8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,
9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,
9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,
9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,
9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,
9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,10009,10037,10039,10061,10067,10069,10079,
10091,10093,10099,10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,10181,10193,10211,10223,10243,
10247,10253,10259,10267,10271,10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,10357,10369,10391,
10399,10427,10429,10433,10453,10457,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,10589,
10597,10601,10607,10613,10627,10631,10639,10651,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733,
10739,10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,10861,10867,10883,10889,10891,10903,10909,
10937,10939,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,11069,11071,11083,11087,11093,
11113,11117,11119,11131,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,11257,11261,11273,
11279,11287,11299,11311,11317,11321,11329,11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,11447,
11467,11471,11483,11489,11491,11497,11503,11519,11527,11549,11551,11579,11587,11593,11597,11617,11621,11633,
11657,11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,11779,11783,11789,11801,11807,11813,11821,
11827,11831,11833,11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,11939,11941,11953,11959,11969,
11971,11981,11987,12007,12011,12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,12113,12119,12143,
12149,12157,12161,12163,12197,12203,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,12301,
12323,12329,12343,12347,12373,12377,12379,12391,12401,12409,12413,12421,12433,12437,12451,12457,12473,12479,
12487,12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,12569,12577,12583,12589,12601,12611,12613,
12619,12637,12641,12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,12743,12757,12763,12781,12791,
12799,12809,12821,12823,12829,12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,12941,12953,12959,
12967,12973,12979,12983,13001,13003,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,13121,
13127,13147,13151,13159,13163,13171,13177,13183,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297,
13309,13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,
13477,13487,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,
13681,13687,13691,13693,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,13789,13799,13807,
13829,13831,13841,13859,13873,13877,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,13997,
13999,14009,14011,14029,14033,14051,14057,14071,14081,14083,14087,14107,14143,14149,14153,14159,14173,14177,
14197,14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,14327,14341,14347,14369,14387,14389,14401,
14407,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,14533,14537,14543,14549,14551,
14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,14713,14717,14723,
14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,14867,
14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14957,14969,14983,15013,15017,15031,15053,15061,
15073,15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,15161,15173,15187,15193,15199,15217,15227,
15233,15241,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,15329,15331,15349,15359,15361,
15373,15377,15383,15391,15401,15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,15511,15527,15541,
15551,15559,15569,15581,15583,15601,15607,15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,15683,
15727,15731,15733,15737,15739,15749,15761,15767,15773,15787,15791,15797,15803,15809,15817,15823,15859,15877,
15881,15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,15973,15991,16001,16007,16033,16057,16061,
16063,16067,16069,16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,16187,16189,16193,16217,16223,
16229,16231,16249,16253,16267,16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,16421,
16427,16433,16447,16451,16453,16477,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573,16603,16607,
16619,16631,16633,16649,16651,16657,16661,16673,16691,16693,16699,16703,16729,16741,16747,16759,16763,16787,
16811,16823,16829,16831,16843,16871,16879,16883,16889,16901,16903,16921,16927,16931,16937,16943,16963,16979,
16981,16987,16993,17011,17021,17027,17029,17033,17041,17047,17053,17077,17093,17099,17107,17117,17123,17137,
17159,17167,17183,17189,17191,17203,17207,17209,17231,17239,17257,17291,17293,17299,17317,17321,17327,17333,
17341,17351,17359,17377,17383,17387,17389,17393,17401,17417,17419,17431,17443,17449,17467,17471,17477,17483,
17489,17491,17497,17509,17519,17539,17551,17569,17573,17579,17581,17597,17599,17609,17623,17627,17657,17659,
17669,17681,17683,17707,17713,17729,17737,17747,17749,17761,17783,17789,17791,17807,17827,17837,17839,17851,
17863,17881,17891,17903,17909,17911,17921,17923,17929,17939,17957,17959,17971,17977,17981,17987,17989,18013,
18041,18043,18047,18049,18059,18061,18077,18089,18097,18119,18121,18127,18131,18133,18143,18149,18169,18181,
18191,18199,18211,18217,18223,18229,18233,18251,18253,18257,18269,18287,18289,18301,18307,18311,18313,18329,
18341,18353,18367,18371,18379,18397,18401,18413,18427,18433,18439,18443,18451,18457,18461,18481,18493,18503,
18517,18521,18523,18539,18541,18553,18583,18587,18593,18617,18637,18661,18671,18679,18691,18701,18713,18719,
18731,18743,18749,18757,18773,18787,18793,18797,18803,18839,18859,18869,18899,18911,18913,18917,18919,18947,
18959,18973,18979,19001,19009,19013,19031,19037,19051,19069,19073,19079,19081,19087,19121,19139,19141,19157,
19163,19181,19183,19207,19211,19213,19219,19231,19237,19249,19259,19267,19273,19289,19301,19309,19319,19333,
19373,19379,19381,19387,19391,19403,19417,19421,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471,
19477,19483,19489,19501,19507,19531,19541,19543,19553,19559,19571,19577,19583,19597,19603,19609,19661,19681,
19687,19697,19699,19709,19717,19727,19739,19751,19753,19759,19763,19777,19793,19801,19813,19819,19841,19843,
19853,19861,19867,19889,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,19993,19997,20011,
20021,20023,20029,20047,20051,20063,20071,20089,20101,20107,20113,20117,20123,20129,20143,20147,20149,20161,
20173,20177,20183,20201,20219,20231,20233,20249,20261,20269,20287,20297,20323,20327,20333,20341,20347,20353,
20357,20359,20369,20389,20393,20399,20407,20411,20431,20441,20443,20477,20479,20483,20507,20509,20521,20533,
20543,20549,20551,20563,20593,20599,20611,20627,20639,20641,20663,20681,20693,20707,20717,20719,20731,20743,
20747,20749,20753,20759,20771,20773,20789,20807,20809,20849,20857,20873,20879,20887,20897,20899,20903,20921,
20929,20939,20947,20959,20963,20981,20983,21001,21011,21013,21017,21019,21023,21031,21059,21061,21067,21089,
21101,21107,21121,21139,21143,21149,21157,21163,21169,21179,21187,21191,21193,21211,21221,21227,21247,21269,
21277,21283,21313,21317,21319,21323,21341,21347,21377,21379,21383,21391,21397,21401,21407,21419,21433,21467,
21481,21487,21491,21493,21499,21503,21517,21521,21523,21529,21557,21559,21563,21569,21577,21587,21589,21599,
21601,21611,21613,21617,21647,21649,21661,21673,21683,21701,21713,21727,21737,21739,21751,21757,21767,21773,
21787,21799,21803,21817,21821,21839,21841,21851,21859,21863,21871,21881,21893,21911,21929,21937,21943,21961,
21977,21991,21997,22003,22013,22027,22031,22037,22039,22051,22063,22067,22073,22079,22091,22093,22109,22111,
22123,22129,22133,22147,22153,22157,22159,22171,22189,22193,22229,22247,22259,22271,22273,22277,22279,22283,
22291,22303,22307,22343,22349,22367,22369,22381,22391,22397,22409,22433,22441,22447,22453,22469,22481,22483,
22501,22511,22531,22541,22543,22549,22567,22571,22573,22613,22619,22621,22637,22639,22643,22651,22669,22679,
22691,22697,22699,22709,22717,22721,22727,22739,22741,22751,22769,22777,22783,22787,22807,22811,22817,22853,
22859,22861,22871,22877,22901,22907,22921,22937,22943,22961,22963,22973,22993,23003,23011,23017,23021,23027,
23029,23039,23041,23053,23057,23059,23063,23071,23081,23087,23099,23117,23131,23143,23159,23167,23173,23189,
23197,23201,23203,23209,23227,23251,23269,23279,23291,23293,23297,23311,23321,23327,23333,23339,23357,23369,
23371,23399,23417,23431,23447,23459,23473,23497,23509,23531,23537,23539,23549,23557,23561,23563,23567,23581,
23593,23599,23603,23609,23623,23627,23629,23633,23663,23669,23671,23677,23687,23689,23719,23741,23743,23747,
23753,23761,23767,23773,23789,23801,23813,23819,23827,23831,23833,23857,23869,23873,23879,23887,23893,23899,
23909,23911,23917,23929,23957,23971,23977,23981,23993,24001,24007,24019,24023,24029,24043,24049,24061,24071,
24077,24083,24091,24097,24103,24107,24109,24113,24121,24133,24137,24151,24169,24179,24181,24197,24203,24223,
24229,24239,24247,24251,24281,24317,24329,24337,24359,24371,24373,24379,24391,24407,24413,24419,24421,24439,
24443,24469,24473,24481,24499,24509,24517,24527,24533,24547,24551,24571,24593,24611,24623,24631,24659,24671,
24677,24683,24691,24697,24709,24733,24749,24763,24767,24781,24793,24799,24809,24821,24841,24847,24851,24859,
24877,24889,24907,24917,24919,24923,24943,24953,24967,24971,24977,24979,24989,25013,25031,25033,25037,25057,
25073,25087,25097,25111,25117,25121,25127,25147,25153,25163,25169,25171,25183,25189,25219,25229,25237,25243,
25247,25253,25261,25301,25303,25307,25309,25321,25339,25343,25349,25357,25367,25373,25391,25409,25411,25423,
25439,25447,25453,25457,25463,25469,25471,25523,25537,25541,25561,25577,25579,25583,25589,25601,25603,25609,
25621,25633,25639,25643,25657,25667,25673,25679,25693,25703,25717,25733,25741,25747,25759,25763,25771,25793,
25799,25801,25819,25841,25847,25849,25867,25873,25889,25903,25913,25919,25931,25933,25939,25943,25951,25969,
25981,25997,25999,26003,26017,26021,26029,26041,26053,26083,26099,26107,26111,26113,26119,26141,26153,26161,
26171,26177,26183,26189,26203,26209,26227,26237,26249,26251,26261,26263,26267,26293,26297,26309,26317,26321,
26339,26347,26357,26371,26387,26393,26399,26407,26417,26423,26431,26437,26449,26459,26479,26489,26497,26501,
26513,26539,26557,26561,26573,26591,26597,26627,26633,26641,26647,26669,26681,26683,26687,26693,26699,26701,
26711,26713,26717,26723,26729,26731,26737,26759,26777,26783,26801,26813,26821,26833,26839,26849,26861,26863,
26879,26881,26891,26893,26903,26921,26927,26947,26951,26953,26959,26981,26987,26993,27011,27017,27031,27043,
27059,27061,27067,27073,27077,27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,27239,27241,27253,
27259,27271,27277,27281,27283,27299,27329,27337,27361,27367,27397,27407,27409,27427,27431,27437,27449,27457,
27479,27481,27487,27509,27527,27529,27539,27541,27551,27581,27583,27611,27617,27631,27647,27653,27673,27689,
27691,27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,27773,27779,27791,27793,27799,27803,27809,
27817,27823,27827,27847,27851,27883,27893,27901,27917,27919,27941,27943,27947,27953,27961,27967,27983,27997,
28001,28019,28027,28031,28051,28057,28069,28081,28087,28097,28099,28109,28111,28123,28151,28163,28181,28183,
28201,28211,28219,28229,28277,28279,28283,28289,28297,28307,28309,28319,28349,28351,28387,28393,28403,28409,
28411,28429,28433,28439,28447,28463,28477,28493,28499,28513,28517,28537,28541,28547,28549,28559,28571,28573,
28579,28591,28597,28603,28607,28619,28621,28627,28631,28643,28649,28657,28661,28663,28669,28687,28697,28703,
28711,28723,28729,28751,28753,28759,28771,28789,28793,28807,28813,28817,28837,28843,28859,28867,28871,28879,
28901,28909,28921,28927,28933,28949,28961,28979,29009,29017,29021,29023,29027,29033,29059,29063,29077,29101,
29123,29129,29131,29137,29147,29153,29167,29173,29179,29191,29201,29207,29209,29221,29231,29243,29251,29269,
29287,29297,29303,29311,29327,29333,29339,29347,29363,29383,29387,29389,29399,29401,29411,29423,29429,29437,
29443,29453,29473,29483,29501,29527,29531,29537,29567,29569,29573,29581,29587,29599,29611,29629,29633,29641,
29663,29669,29671,29683,29717,29723,29741,29753,29759,29761,29789,29803,29819,29833,29837,29851,29863,29867,
29873,29879,29881,29917,29921,29927,29947,29959,29983,29989,30011,30013,30029,30047,30059,30071,30089,30091,
30097,30103,30109,30113,30119,30133,30137,30139,30161,30169,30181,30187,30197,30203,30211,30223,30241,30253,
30259,30269,30271,30293,30307,30313,30319,30323,30341,30347,30367,30389,30391,30403,30427,30431,30449,30467,
30469,30491,30493,30497,30509,30517,30529,30539,30553,30557,30559,30577,30593,30631,30637,30643,30649,30661,
30671,30677,30689,30697,30703,30707,30713,30727,30757,30763,30773,30781,30803,30809,30817,30829,30839,30841,
30851,30853,30859,30869,30871,30881,30893,30911,30931,30937,30941,30949,30971,30977,30983,31013,31019,31033,
31039,31051,31063,31069,31079,31081,31091,31121,31123,31139,31147,31151,31153,31159,31177,31181,31183,31189,
31193,31219,31223,31231,31237,31247,31249,31253,31259,31267,31271,31277,31307,31319,31321,31327,31333,31337,
31357,31379,31387,31391,31393,31397,31469,31477,31481,31489,31511,31513,31517,31531,31541,31543,31547,31567,
31573,31583,31601,31607,31627};
const unsigned short Droots[] = {
2,3,5,7,2,4,8,10,5,11,4,10,5,7,11,8,14,7,13,8,10,16,11,17,16,2,4,8,10,5,10,5,11,13,14,7,
13,10,14,11,17,10,11,13,17,19,4,7,11,13,8,14,7,8,14,11,17,10,16,11,13,14,10,5,7,11,7,13,14,16,11,
17,16,13,19,14,20,19,5,13,14,7,8,10,16,11,17,16,11,13,17,20,19,14,22,8,14,8,10,10,16,17,14,20,13,19,
20,17,23,7,13,10,14,16,10,11,13,17,14,20,13,16,20,17,16,8,16,17,16,13,19,14,13,19,14,22,17,22,23,17,10,
11,13,17,19,20,16,20,22,17,22,17,19,23,16,11,19,20,19,14,20,17,22,17,23,20,19,25,10,5,11,4,5,7,13,14,
7,8,10,16,16,11,13,17,5,11,10,7,13,8,10,11,10,11,17,14,4,7,11,8,14,7,13,16,17,17,19,14,20,13,19,
5,7,11,14,7,13,11,17,14,13,22,14,10,14,16,11,17,16,11,13,19,13,14,16,20,22,17,23,8,11,10,13,19,14,20,
19,14,22,17,22,8,14,16,11,17,10,16,17,19,16,20,22,19,23,25,17,11,13,14,13,19,16,22,22,19,23,25,10,11,14,
13,20,16,22,17,19,23,25,26,11,17,14,14,16,23,16,20,26,25,22,26,28,5,4,10,11,13,14,10,11,17,11,13,17,19,
20,5,7,14,7,13,8,10,11,10,19,7,11,8,7,14,16,11,10,17,19,14,13,19,16,20,14,7,11,17,10,16,11,17,13,
19,14,16,22,17,23,8,14,11,16,11,17,20,19,16,20,10,10,11,19,14,20,13,19,23,17,19,17,16,11,14,19,20,22,17,
16,22,19,23,25,20,26,16,11,13,19,20,13,14,22,17,22,23,26,19,25,11,13,20,16,20,17,16,22,17,26,25,26,14,20,
19,20,23,19,23,20,26,19,29,4,5,13,8,13,8,16,10,16,19,14,20,13,14,7,14,13,17,19,13,19,14,8,14,13,8,
16,11,13,17,19,13,23,7,13,10,16,11,17,10,13,17,20,13,14,16,23,16,14,11,13,20,19,14,16,20,22,17,25,10,16,
17,19,14,20,13,19,20,22,16,17,19,20,16,13,17,14,13,19,16,23,17,19,23,19,25,11,19,20,19,16,22,17,23,25,26,
22,26,14,14,16,17,22,17,19,20,25,20,28,19,14,20,22,17,23,16,19,23,25,29,5,7,11,8,14,7,13,17,10,16,14,
20,14,16,22,7,14,16,11,17,13,17,19,19,7,8,14,16,17,10,11,13,14,20,13,14,16,17,23,22,16,17,19,20,19,16,
17,17,23,17,11,13,13,19,14,20,17,17,19,20,16,13,17,19,14,20,22,16,22,20,19,25,13,13,20,22,17,23,16,22,19,
20,26,20,14,14,16,22,17,17,25,22,26,28,23,29,13,16,20,16,19,20,26,29,16,22,23,17,19,23,20,19,25,26,28,23,
28,25,31,8,14,7,8,10,17,11,19,19,14,20,23,7,13,10,16,17,14,19,14,22,23,22,16,16,11,13,17,14,17,23,16,
23,11,17,13,14,19,14,17,23,20,26,16,13,17,19,13,19,14,16,22,17,23,25,20,11,13,17,20,13,19,14,22,19,25,20,
19,20,16,23,16,22,17,19,23,25,26,22,28,23,13,14,20,22,17,19,25,28,23,22,14,20,17,16,22,25,20,26,19,25,20,
26,28,29,22,29,17,19,23,26,22,23,29,13,8,17,16,13,17,14,19,16,22,23,16,8,11,10,11,13,14,13,16,17,23,25,
11,10,16,11,19,19,20,17,23,16,22,23,26,10,11,17,14,20,19,16,17,23,16,22,19,25,26,25,13,19,23,16,25,20,19,
20,14,22,22,17,19,20,26,19,25,20,29,19,22,22,20,26,19,22,28,29,22,14,16,22,23,19,23,20,22,29,22,23,25,17,
19,23,25,20,19,26,23,29,22,25,32,22,17,23,26,28,29,22,28,23,29,26,25,31,8,11,17,16,19,14,19,22,23,11,17,
11,17,19,14,22,22,23,20,16,11,13,19,20,19,16,20,17,20,25,17,19,13,14,16,23,16,25,22,13,19,17,17,23,25,25,
20,26,28,29,19,20,17,23,22,17,23,25,26,19,22,26,23,29,22,16,20,16,25,20,26,28,23,22,28,23,31,17,22,19,23,
19,22,26,28,31,26,23,20,26,20,23,28,25,29,31,26,17,23,26,25,22,26,29,22,25,28,17,10,16,20,16,22,23,17,23,
25,20,10,11,17,14,20,16,22,17,25,19,19,20,13,14,16,20,17,19,25,20,25,20,22,26,13,19,22,19,20,26,25,26,28,
22,17,23,16,19,23,19,25,14,17,16,22,23,25,20,22,23,22,29,31,23,19,23,25,19,25,23,29,28,23,31,26,32,22,19,
25,19,25,20,26,23,22,31,26,19,23,26,19,20,26,28,29,23,25,29,31,28,22,28,23,22,23,26,32,25,35,10,16,11,13,
20,14,16,22,23,22,19,13,19,19,16,20,16,22,17,20,19,25,28,14,20,14,20,23,16,23,25,20,22,23,14,22,17,22,17,
19,25,20,26,22,28,16,17,23,16,17,19,23,25,20,22,26,23,29,23,29,16,17,20,26,25,20,29,16,19,25,20,26,19,22,
28,22,29,31,32,31,26,19,22,28,23,29,29,31,25,31,26,20,19,25,28,23,29,23,29,31,25,28,32,19,25,23,29,22,23,
31,31,28,8,10,11,13,8,14,16,17,11,13,19,5,4,8,14,7,8,16,11,17,16,11,14,5,8,10,14,11,17,16,11,13,
20,5,7,8,7,8,10,14,11,16,19,14,22,14,16,11,13,17,19,14,19,20,23,7,10,17,10,20,19,23,22,8,14,11,16,
11,19,13,19,16,20,22,17,17,10,13,19,14,20,16,16,17,25,26,13,19,20,17,23,16,22,20,26,19,13,19,20,22,23,22,
20,26,25,22,5,11,13,14,16,17,10,13,17,14,7,11,13,7,16,17,10,11,13,17,19,8,16,11,10,16,11,14,20,19,22,
7,13,8,16,11,13,20,16,17,23,8,11,16,13,17,19,14,17,23,16,22,10,17,16,20,13,23,22,19,23,16,11,14,20,22,
17,25,26,10,17,19,13,16,23,25,20,26,11,17,14,13,19,14,16,22,19,23,25,26,14,20,16,20,17,23,16,19,25,26,19,
20,26,10,5,13,8,10,16,11,13,19,5,11,13,8,14,11,17,16,11,13,20,8,7,14,17,10,11,13,14,20,19,14,22,7,
11,17,13,17,16,20,22,16,8,16,11,10,13,17,13,19,17,23,22,17,23,11,10,16,17,20,13,19,16,23,22,19,25,10,11,
13,19,19,14,20,17,23,17,26,25,13,14,13,22,17,22,19,19,20,28,20,14,16,22,16,19,28,23,29,19,14,20,22,17,17,
20,26,25,22,28,23,5,7,11,13,10,14,11,17,13,16,22,8,14,8,14,16,11,19,14,13,19,16,20,14,16,17,11,19,20,
19,16,22,16,11,16,11,17,19,20,16,23,25,10,16,11,13,14,20,17,23,22,23,26,13,14,19,17,22,23,19,25,14,20,19,
16,23,25,26,19,25,20,22,26,20,13,14,16,22,17,23,25,20,20,28,29,19,23,16,17,26,22,26,28,23,14,16,20,17,16,
17,19,22,26,29,31,14,7,16,11,11,17,13,14,16,20,13,13,19,14,20,16,20,22,14,10,14,20,13,16,19,11,11,13,17,
13,19,23,23,25,10,16,11,19,14,13,19,20,22,16,25,26,13,20,16,20,17,23,16,22,17,19,20,22,14,20,22,17,23,19,
23,26,22,29,16,20,17,16,22,17,23,20,26,25,20,28,23,28,17,16,22,17,20,19,26,28,29,28,23,29,19,25,26,25,20,
26,29,25,10,14,10,14,13,16,20,17,16,8,14,10,11,17,19,20,14,17,22,19,25,16,17,14,13,22,17,23,16,22,23,25,
26,16,13,19,20,13,22,23,16,19,23,20,19,11,14,19,22,17,16,17,23,20,22,26,13,20,16,17,25,26,20,22,13,19,22,
23,17,19,23,25,19,25,20,28,23,22,17,19,23,25,26,20,26,23,28,23,29,17,23,22,19,28,28,23,29,31,16,22,19,25,
20,25,29,23,25,25,8,14,13,19,14,16,20,22,17,22,17,23,11,10,17,20,13,19,23,25,20,17,14,20,13,22,17,22,19,
11,20,16,22,23,17,19,25,19,13,19,14,20,17,22,17,19,25,20,26,23,22,23,23,20,19,25,22,16,20,23,17,19,26,19,
25,20,23,23,25,31,17,25,19,25,28,23,29,17,20,26,19,22,23,31,26,32,17,19,19,25,20,26,23,25,32,25,31,28,10,
11,17,19,14,13,19,16,22,20,26,16,17,14,19,23,22,20,26,19,13,17,19,14,22,22,20,22,28,19,14,20,17,16,17,25,
25,22,26,28,23,13,20,22,16,19,25,25,20,26,23,29,22,28,22,23,25,19,28,23,29,22,29,31,23,19,23,26,28,29,23,
25,22,19,26,25,26,28,22,26,32,25,23,25,26,28,22,25,25,26,20,26,19,20,22,28,29,29,31,25,31,26,32,34,13,14,
16,20,22,23,16,23,26,25,20,13,19,14,16,17,23,25,19,20,28,13,19,16,22,17,17,19,23,26,26,28,13,19,14,16,23,
17,20,25,20,28,28,14,17,22,19,25,20,19,25,20,22,25,17,22,17,19,26,19,22,25,29,26,23,25,22,23,31,25,17,20,
26,20,23,29,28,26,31,28,32,20,29,31,32,35,20,22,26,28,29,32,28,34,11,19,14,14,20,16,25,20,26,19,25,14,23,
16,23,20,20,22,19,14,16,22,16,22,25,26,25,22,29,14,22,23,19,23,29,22,28,23,17,22,17,19,23,25,20,19,25,26,
23,29,22,28,25,31,16,22,19,20,22,23,29,23,29,26,31,19,25,23,25,31,32,34,26,25,26,29,23,25,31,26,31,29,19,
22,28,23,25,26,25,31,35,28,23,29,28,29,32,26,28,29,35,29,31,35,4,5,7,13,13,8,11,10,19,4,10,7,11,8,
14,10,14,16,10,13,17,14,5,14,8,10,17,11,19,19,20,10,14,11,10,16,13,17,19,20,22,17,23,13,8,10,11,13,20,
22,17,14,16,10,13,14,20,13,16,19,25,10,17,20,13,17,17,20,16,17,19,13,16,20,22,17,23,17,19,26,17,19,23,22,
20,26,25,26,28,14,14,22,23,22,25,20,20,22,4,5,7,11,13,8,7,17,10,16,20,5,11,7,16,11,17,16,13,19,20,
19,14,16,7,8,14,16,20,19,16,10,14,16,11,11,17,20,22,17,16,22,8,14,17,13,20,16,22,17,19,25,11,16,11,13,
19,20,22,17,23,22,23,25,26,10,11,13,17,20,22,16,19,20,11,14,19,20,22,16,22,23,20,25,28,14,19,14,23,16,17,
25,20,19,20,23,14,23,22,19,19,26,22,28,7,8,13,8,14,16,10,13,17,14,20,14,16,14,7,10,16,11,16,13,17,19,
13,22,17,17,17,20,14,16,20,22,17,16,10,14,14,20,20,22,16,17,23,17,14,13,19,16,23,17,19,10,11,13,14,16,22,
22,17,19,14,20,13,20,22,17,16,25,26,20,26,28,20,19,14,20,23,16,17,26,25,22,26,19,14,20,20,26,19,20,26,14,
20,16,23,20,20,22,23,25,8,7,13,8,14,16,17,10,13,17,19,14,13,14,20,23,14,10,13,20,19,16,23,22,8,10,16,
16,13,22,23,17,19,23,10,11,17,14,20,20,23,16,26,17,13,20,23,19,25,19,14,20,22,23,22,17,19,23,19,22,28,14,
20,16,20,22,17,20,26,19,25,26,28,22,17,19,23,20,19,25,22,29,14,17,23,22,17,19,25,28,23,29,28,25,31,23,16,
22,25,26,22,28,23,26,7,13,16,11,17,13,19,13,14,20,17,16,22,10,14,16,11,10,13,17,13,22,23,16,23,11,13,19,
20,19,14,17,17,20,19,23,17,19,25,19,17,14,20,13,22,17,25,20,19,28,20,19,20,17,22,17,19,23,14,17,16,26,20,
26,23,22,28,22,19,26,22,26,22,25,31,23,17,19,25,20,28,28,31,22,23,25,20,22,23,28,23,29,31,32,11,11,13,17,
19,17,22,23,10,16,11,17,19,16,17,23,16,19,25,19,20,19,16,20,17,16,11,13,17,19,13,22,17,23,22,23,20,20,20,
13,16,23,22,19,23,20,26,19,17,22,17,19,26,28,23,29,14,16,22,16,19,25,20,25,26,23,29,25,17,22,20,19,25,28,
23,22,26,32,16,25,20,26,28,28,25,32,19,20,26,20,22,28,23,22,31,25,32,34,11,16,11,19,13,16,19,26,16,11,13,
19,14,17,16,17,23,20,26,13,19,19,20,23,16,17,19,23,22,26,20,19,14,23,22,23,19,26,23,29,19,20,17,16,22,25,
26,28,29,28,14,17,25,25,20,23,23,29,23,20,19,25,29,23,25,29,26,32,16,17,19,23,20,26,19,25,29,29,26,17,20,
19,22,28,29,23,25,32,25,26,28,20,20,26,28,23,25,31,26,32,29,11,17,13,16,23,16,22,19,23,19,13,17,19,19,17,
26,20,26,13,23,16,19,25,19,25,20,22,29,23,22,19,25,28,20,22,22,17,23,26,25,29,22,28,23,23,25,26,19,20,23,
25,17,23,19,26,23,25,32,25,31,17,22,26,28,23,29,22,25,29,26,32,26,28,34,20,26,25,22,26,28,23,28,29,19,26,
28,23,25,29,26,25,31,29,34,11,20,19,14,16,22,25,19,25,26,28,20,13,16,17,20,20,22,13,14,22,23,26,28,23,29,
28,20,22,23,26,19,28,25,17,23,16,25,20,26,25,23,28,26,32,19,23,25,20,26,28,29,23,25,31,25,31,19,23,26,19,
25,20,23,29,28,23,25,31,31,32,20,19,22,28,23,25,31,25,34,29,25,22,26,28,25,32,31,26,34,20,28,22,28,25,32,
26,35,20,19,14,16,20,17,25,20,25,13,17,23,16,22,23,20,25,22,28,22,14,20,22,16,17,20,19,28,28,29,17,16,23,
20,26,25,23,25,29,31,32,16,17,20,26,25,22,23,25,26,17,25,20,26,29,31,26,25,31,34,19,28,23,22,26,32,25,28,
26,23,23,26,32,25,35,22,29,25,29,25,28,32,29,35,28,28,23,29,31,34,31,37,5,7,14,14,17,11,20,13,19,7,13,
8,14,10,14,16,11,19,13,19,20,8,7,10,10,13,19,20,13,17,13,10,16,11,11,17,19,23,16,10,16,11,20,20,22,17,
19,23,17,16,19,20,16,20,22,22,20,13,19,16,22,16,17,23,26,25,13,17,14,19,22,19,20,19,14,20,19,22,23,16,17,
19,25,26,19,20,23,14,16,22,17,25,20,26,23,8,14,10,16,10,13,19,20,13,14,8,10,17,16,11,13,19,19,14,16,22,
17,16,11,10,16,17,19,14,20,19,14,20,14,17,10,16,13,17,19,23,22,17,19,23,23,22,17,25,11,13,17,13,14,16,20,
22,19,20,11,17,19};	

const short pre_calc = 1376; 
const LONG SmithNumber[pre_calc] = {
4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535,
562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895,
913, 915, 922, 958, 985, 1086, 1111, 1165, 1219, 1255, 1282, 1284, 1376, 1449, 1507, 1581, 1626, 1633, 1642,
1678, 1736, 1755, 1776, 1795, 1822, 1842, 1858, 1872, 1881, 1894, 1903, 1908, 1921, 1935, 1952, 1962, 1966,
2038, 2067, 2079, 2155, 2173, 2182, 2218, 2227, 2265, 2286, 2326, 2362, 2366, 2373, 2409, 2434, 2461, 2475,
2484, 2515, 2556, 2576, 2578, 2583, 2605, 2614, 2679, 2688, 2722, 2745, 2751, 2785, 2839, 2888, 2902, 2911,
2934, 2944, 2958, 2964, 2965, 2970, 2974, 3046, 3091, 3138, 3168, 3174, 3226, 3246, 3258, 3294, 3345, 3366,
3390, 3442, 3505, 3564, 3595, 3615, 3622, 3649, 3663, 3690, 3694, 3802, 3852, 3864, 3865, 3930, 3946, 3973,
4054, 4126, 4162, 4173, 4185, 4189, 4191, 4198, 4209, 4279, 4306, 4369, 4414, 4428, 4464, 4472, 4557, 4592,
4594, 4702, 4743, 4765, 4788, 4794, 4832, 4855, 4880, 4918, 4954, 4959, 4960, 4974, 4981, 5062, 5071, 5088,
5098, 5172, 5242, 5248, 5253, 5269, 5298, 5305, 5386, 5388, 5397, 5422, 5458, 5485, 5526, 5539, 5602, 5638,
5642, 5674, 5772, 5818, 5854, 5874, 5915, 5926, 5935, 5936, 5946, 5998, 6036, 6054, 6084, 6096, 6115, 6171,
6178, 6187, 6188, 6252, 6259, 6295, 6315, 6344, 6385, 6439, 6457, 6502, 6531, 6567, 6583, 6585, 6603, 6684,
6693, 6702, 6718, 6760, 6816, 6835, 6855, 6880, 6934, 6981, 7026, 7051, 7062, 7068, 7078, 7089, 7119, 7136,
7186, 7195, 7227, 7249, 7287, 7339, 7402, 7438, 7447, 7465, 7503, 7627, 7674, 7683, 7695, 7712, 7726, 7762,
7764, 7782, 7784, 7809, 7824, 7834, 7915, 7952, 7978, 8005, 8014, 8023, 8073, 8077, 8095, 8149, 8154, 8158,
8185, 8196, 8253, 8257, 8277, 8307, 8347, 8372, 8412, 8421, 8466, 8518, 8545, 8568, 8628, 8653, 8680, 8736,
8754, 8766, 8790, 8792, 8851, 8864, 8874, 8883, 8901, 8914, 9015, 9031, 9036, 9094, 9166, 9184, 9193, 9229,
9274, 9276, 9285, 9294, 9296, 9301, 9330, 9346, 9355, 9382, 9386, 9387, 9396, 9414, 9427, 9483, 9522, 9535,
9571, 9598, 9633, 9634, 9639, 9648, 9657, 9684, 9708, 9717, 9735, 9742, 9760, 9778, 9840, 9843, 9849, 9861,
9880, 9895, 9924, 9942, 9968, 9975, 9985,10086,10201,10291,10296,10419,10462,10489,10494,10579,10592,10606,
10664,10669,10689,10698,10705,
10736,10761,10786,10791,10797,10806,10845,10887,10966,11065,11209,11358,11385,11388,11583,
11659,11679,11686,11695,11696,11739,11785,11790,11816,11857,11965,11984,12055,12091,12226,
12262,12318,12406,12442,12519,12558,12573,12622,12627,12648,12656,12658,12667,12675,12684,
12732,12771,12795,12847,12937,12939,12946,12955,12957,12975,12982,13369,13454,13472,13506,
13639,13662,13666,13747,13764,13765,13812,13905,13974,13984,14017,14026,14046,14058,14085,
14148,14168,14179,14206,14242,14359,14386,14391,14422,14458,14464,14494,14508,14534,14566,
14672,14688,14719,14736,14756,14784,14809,14832,14881,14924,14946,14958,14962,14985,14991,
14998,15018,15115,15126,15128,15205,15286,15369,15516,15529,15558,15646,15682,15687,15704,
15709,15747,15778,15824,15835,15848,15853,15860,15882,15884,15894,15898,15943,15974,15981,
15984,16015,16078,16098,16105,16123,16137,16186,16192,16222,16269,16285,16294,16335,16357,
16438,16474,16480,16536,16537,16546,16568,16582,16591,16592,16645,16647,16653,16688,16726,
16735,16744,16746,16770,16866,16890,16902,16940,16983,17056,17086,17149,17187,17199,17221,
17238,17268,17271,17424,17455,17482,17496,17635,17646,17662,17664,17698,17718,17738,17754,
17826,17833,17835,17838,17840,17864,17885,17889,17905,17907,17916,17940,17982,18022,18058,
18069,18085,18108,18117,18132,18162,18177,18247,18274,18278,18337,18346,18355,18391,18396,
18409,18418,18454,18459,18474,18496,18513,18562,18607,18618,18675,18732,18735,18742,18765,
18805,18841,18846,18865,18872,18895,18920,18922,18958,18963,18985,18994,19066,19134,19147,
19165,19212,19232,19246,19251,19255,19272,19280,19292,19360,19376,19428,19482,19498,19554,
19590,19592,19602,19606,19615,19644,19678,19683,19725,19755,19761,19808,19812,19818,19858,
19880,19941,19943,19952,20065,20074,20182,20229,20295,20299,20319,20326,20362,20506,20542,
20578,20618,20623,20695,20754,20784,20785,20823,20859,20888,20893,20911,20974,21055,21066,
21078,21186,21226,21253,21262,21273,21361,21478,21498,21615,21651,21667,21685,21694,21766,
21829,21865,21874,21896,21919,21946,21955,21970,22054,22081,22117,22119,22188,22234,22342,
22368,22386,22448,22509,22522,22558,22585,22688,22702,22725,22734,22738,22816,22837,22884,
22971,22983,23089,23098,23163,23192,23242,23343,23449,23484,23566,23577,23602,23658,23665,
23694,23736,23755,23775,23790,23809,23818,23854,23870,23953,23962,24096,24142,24214,24259,
24306,24322,24354,24387,24394,24403,24502,24538,24552,24585,24588,24637,24655,24678,24754,
24776,24828,24928,24945,24954,24963,24981,25006,25015,25064,25078,25105,25177,25195,25197,
25222,25236,25256,25263,25267,25294,25298,25392,25398,25428,25429,25573,25582,25614,25618,
25735,25798,25807,25809,25834,25844,25884,25893,25906,25928,26014,26096,26167,26185,26277,
26292,26295,26302,26365,26367,26374,26394,26397,26419,26475,26480,26518,26527,26545,26558,
26637,26660,26676,26682,26707,26709,26727,26734,26760,26768,26781,26826,26840,26892,26905,
26914,26943,26995,26999,27045,27049,27085,27156,27189,27193,27209,27238,27247,27261,27267,
27270,27280,27285,27296,27319,27321,27355,27357,27382,27418,27468,27526,27535,27546,27555,
27562,27589,27598,27621,27639,27666,27696,27756,27768,27792,27804,27814,27828,27846,27855,
27882,27915,27950,27994,28039,28068,28102,28174,28182,28208,28236,28255,28280,28284,28318,
28336,28354,28380,28392,28449,28574,28595,28635,28662,28705,28716,28749,28784,28808,28809,
28833,28840,28849,28905,28920,28952,28960,28980,29038,29065,29074,29078,29139,29166,29172,
29182,29193,29227,29254,29265,29344,29364,29371,29398,29424,29434,29456,29461,29484,29506,
29515,29529,29538,29540,29542,29551,29565,29583,29607,29623,29624,29634,29695,29706,29748,
29758,29760,29772,29794,29826,29890,29893,29902,29938,29960,30055,30138,30258,30262,30288,
30298,30384,30390,30393,30397,30505,30523,30658,30687,30739,30766,30802,30811,30865,30879,
30906,30930,30946,30957,30991,31096,31099,31119,31257,31476,31488,31585,31598,31639,31648,
31693,31724,31746,31765,31846,31956,31959,31976,31980,32017,32118,32197,32206,32226,32278,
32283,32386,32418,32454,32458,32552,32593,32602,32638,32648,32696,32697,32724,32755,32786,
32793,32827,32854,32883,32896,32899,32962,32976,32982,32989,32991,33027,33045,33056,33063,
33090,33097,33169,33315,33378,33384,33387,33462,33486,33528,33585,33632,33633,33635,33646,
33657,33669,33672,33680,33727,33747,33760,33862,33880,33907,33918,33992,34042,34051,34182,
34186,34249,34317,34339,34359,34366,34395,34424,34458,34555,34575,34582,34609,34654,34663,
34717,34776,34784,34832,34834,34861,34942,34956,34978,34987,35005,35095,35187,35239,35293,
35358,35364,35383,35397,35432,35466,35469,35478,35538,35545,35547,35594,35635,35680,35696,
35745,35775,35784,35790,35793,35796,35805,35806,35842,35878,35979,36090,36094,36099,36139,
36193,36238,36265,36296,36306,36335,36382,36393,36409,36464,36481,36498,36535,36537,36555,
36654,36680,36706,36742,36762,36870,36876,36890,36922,36990,37095,37098,37129,37165,37167,
37180,37237,37255,37374,37383,37426,37462,37476,37482,37498,37560,37592,37606,37615,37651,
37671,37678,37705,37743,37795,37820,37822,37840,37848,37885,37894,37903,37960,38002,38029,
38074,38137,38146,38168,38238,38263,38283,38286,38326,38362,38385,38388,38402,38440,38490,
38515,38560,38562,38578,38589,38641,38675,38758,38785,38817,38864,38871,38911,38925,38938,
38955,38965,38976,39030,39073,39082,39084,39127,39138,39183,39253,39255,39258,39260,39271,
39307,39318,39347,39426,39432,39435,39456,39471,39478,39492,39505,39523,39536,39560,39570,
39579,39585,39586,39595,39597,39642,39650,39678,39685,39711,39720,39757,39780,39792,39811,
39838,39874,39935,39946,39982,39984,40083,40119,40126,40234,40398,40477,40518,40522,40548,
40567,40585,40587,40594,40672,40711,40713,40738,40796,40855,40909,40938,40954,40981,41089,
41098,41278,41359,41376,41386,41436,41494,41557,41624,41678,41699,41746,41757,41829,41892,
41917,41926,41962,41973,42034,42063,42079,42138,42178,42214,42272,42276,42358,42416,42493,
42495,42538,42565,42657,42688,42691,42754,42765,42774};

const LONG sz = 3402; // prime less than sqrt(10^9)

LONG DigitRoot(LONG N) {
	LONG sum = 0;
	for (; N; N /= 10)
		sum += N % 10;
	return sum;
}

bool IsSmithNumber(LONG N) {
	if(binary_search(primes, primes+sz, N) == true) return false;
	else {
		LONG V = DigitRoot(N);
		LONG R = 0;
		const LONG *up = lower_bound(primes, primes+sz, ceil(sqrt(N)));
		short idx = (short)((LONG)up-(LONG)primes)/sizeof(LONG);
		while (N > 1 && V > R && idx >= 0) {
			if((N%(primes[idx])) == 0) {
				do {// Extract Powers
					N /= primes[idx];
					R += Droots[idx];
				} while(N % primes[idx] == 0 && V > R);
				if(binary_search(primes, primes+idx, N) == true) break;
				up = lower_bound(primes, primes+idx, ceil(sqrt(N)));
				idx = (short)((LONG)up-(LONG)primes)/sizeof(LONG);
			} else idx--;
		}
		if(N > 1 && R > 0 && R <= V) R += DigitRoot(N);
		return (V == R);
	}
}

void NextSmithNumber(LONG& N) {
	if(N <= SmithNumber[pre_calc-2]) 
		N = *(lower_bound(SmithNumber, SmithNumber+pre_calc, N));
	else while(IsSmithNumber(N) == false) N++;
	
}
/*int main () {
	LONG N = 1;
	LONG Count = 0;
	while(N <= 1000000000) {
		NextSmithNumber(N);
		Count++;
		//cout << N << endl;
	}
	//25154060
	cout << Count << endl;
	return 0;
}
*/
int main() {
	LONG N, T;
	ios_base::sync_with_stdio(true);
	stringstream oss,iss;
	iss << cin.rdbuf();
	iss >> T;
	// Get rid of endl problem
	iss >> N;
	NextSmithNumber(++N);
	oss << N;

	while(iss.eof() == false && --T > 0){
		oss << "\n";
		iss >> N;
		NextSmithNumber(++N);
		oss << N;
	}
	cout << oss.str();
	return 0;
}
